Planar diagrams for local invariants of graphs in surfaces

With Kyle Miller. Journal of Knot Theory and its Ramifications, 2019.

In order to apply quantum topology methods to non-planar graphs, we define a planar diagram category that describes the local topology of embeddings of graphs into surfaces. We also discuss an extension of the flow polynomial called the S-polynomial and relate it to the Yamada and Penrose polynomials.




What is Lie algebra cohomology and why should you care?

Expository notes on Lie algebra cohomology. The goal is to build up the theory in as concrete a manner as possible, motivated by basic structure theorems for Lie algebras.